QuestionWrite an exponential equation to model Lime County's declining population, starting with 711,500.
Studdy Solution
STEP 1
Assumptions1. The initial population of Lime County when Leslie moved there was711,500.
. The population one year later is697,270.
3. The population decline is expected to continue at the same rate each year.
4. We are to model the population using an exponential function of the form , where is the population, is the number of years after Leslie moved there, is the initial population, and is the rate of decline.
STEP 2
First, we need to find the rate of decline . We can do this by dividing the population one year later by the initial population.
STEP 3
Now, plug in the given values for the population one year later and the initial population to calculate .
STEP 4
Calculate the value of .
STEP 5
Now that we have the rate of decline , we can write the exponential function that models the population of Lime County. The initial population is the population of Lime County when Leslie first moved there, which is711,500.
STEP 6
Plug in the values for and to write the exponential function.
This is the exponential function that models the population of Lime County , years after Leslie moved there.
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